Astérisque

Astérisque
Title	Astérisque
Discipline	Mathematics
Language	French
Publisher	Société Mathématique de France
Country	France
History	1973–present
Frequency	Irregular
Issn	0303-1179

Astérisque is a series of advanced mathematical monographs and conference proceedings published by the Société Mathématique de France. It collects long research articles, lecture notes, and expository surveys addressing topics in Algebraic Geometry, Analytic Number Theory, Representation Theory, Differential Geometry, and related fields. The series has featured works by leading figures associated with institutions such as the Institut des Hautes Études Scientifiques, the École Normale Supérieure, and the Centre National de la Recherche Scientifique.

History

Astérisque was established in the early 1970s under the aegis of the Société Mathématique de France during a period marked by the consolidation of modern Grothendieck-inspired algebraic techniques. Early editorial leadership included mathematicians affiliated with the Université Paris-Sud and the Collège de France, reflecting strong ties to research networks centered at the Institut des Hautes Études Scientifiques and the Centre de Mathématiques Laurent Schwartz. The series rapidly became a venue for long-form expositions by researchers such as Jean-Pierre Serre, Alexander Grothendieck, Grothendieck's students, and contributors linked to the Bourbaki group. Over subsequent decades Astérisque expanded to encompass proceedings from conferences at venues like the International Congress of Mathematicians, workshops at the Clay Mathematics Institute, and thematic schools associated with the European Mathematical Society.

Scope and Content

Astérisque specializes in substantial mathematical works: monographs, lecture courses, and specialized conference volumes. Typical subjects include advances in Étale Cohomology, developments in Hodge Theory, progress on the Langlands Program, innovations in Symplectic Geometry, and research in Algebraic K-theory. The series also publishes detailed expositions on techniques from Homological Algebra, results in Partial Differential Equations tied to geometric analysis, and surveys in Arithmetic Geometry. Contributors have included recipients of major recognitions such as the Fields Medal, the Abel Prize, and the Coxeter–James Prize, reflecting the series’ centrality to current research communities linked to the Institut Henri Poincaré and the Royal Society.

Publication and Format

Volumes in Astérisque are produced irregularly, often timed to the completion of lecture series or conference proceedings rather than a fixed periodic schedule. Typical issues are substantial in length, often exceeding 100 pages, and are distributed in printed form and, increasingly, through digital platforms maintained by the Société Mathématique de France and partner libraries such as the Bibliothèque nationale de France and university repositories at Université Pierre et Marie Curie and Sorbonne Université. Many volumes include detailed bibliographies and extensive appendices, and several are published as companion volumes to conferences organized by institutions like the Centre International de Rencontres Mathématiques and the Institut Fourier.

Editorial Board and Contributors

The editorial board has traditionally comprised senior mathematicians drawn from French institutions and international research centers, including scholars associated with the CNRS, the École Polytechnique, and the Max Planck Institute for Mathematics. Guest editors often coordinate volumes originating from lecture series by researchers at the Institut des Hautes Études Scientifiques, the Université de Paris, and the Princeton University Department of Mathematics. Contributors range from established figures—such as those connected to René Thom, Jean-Pierre Serre, and Pierre Deligne—to emerging researchers affiliated with programs at the European Research Council and the National Science Foundation.

Notable Volumes and Papers

Astérisque has published landmark texts including extended lecture notes and expository treatments that have influenced directions in algebraic topology and algebraic geometry. Noteworthy volumes have presented developments in the proof techniques related to the Weil Conjectures, systematic expositions of Perverse Sheaves, and comprehensive treatments of topics connected to the Moduli Space of Curves, the Tate Conjecture, and the Birch and Swinnerton-Dyer conjecture. Conference proceedings documenting workshops organized with partners such as the International Centre for Theoretical Physics and the Mathematical Sciences Research Institute have also appeared, capturing material by contributors who later published monographs at institutions including Cambridge University Press and Princeton University Press.

Influence and Reception

Within mathematical communities, Astérisque is regarded as an authoritative source for long-form expositions and advanced lecture series. The series has been cited in work originating from research groups at the Institute for Advanced Study, the Max Planck Institute for Mathematics, and departments at Harvard University and Stanford University, informing subsequent monographs and graduate courses at the University of Oxford and the University of Cambridge. Its influence extends into the shaping of curricula for advanced schools such as those at the Institut Fourier and the Centre International de Rencontres Mathématiques, and it has been referenced in award citations for prizes including the Fields Medal and the Shaw Prize.

Access and Availability

Physical copies are available through academic libraries including the Bibliothèque nationale de France, the holdings of major European universities like Sorbonne Université and Université de Lyon, and research libraries at the Princeton University and University of California, Berkeley. Digital access is provided through the publishing activities of the Société Mathématique de France and institutional repositories at the CNRS and selected university libraries; interlibrary loan and purchase remain common routes for individual researchers. Select volumes have been digitized and mirrored by archives associated with the Digital Mathematics Library initiatives and specialized collections at the Gallica platform.

Category:Mathematics journals